Counting Frameworks of Bipyramids
Jack Southgate
TL;DR
This paper establishes a linear upper bound on the number of volume-equivalent bipyramid frameworks and demonstrates that global volume rigidity is not a generic property of simplicial complexes.
Contribution
It provides the first linear bound on the count of volume-equivalent bipyramid frameworks and reveals that global volume rigidity is not generic.
Findings
Linear upper bound on volume-equivalent bipyramid frameworks
Global volume rigidity is not a generic property
Insights into the rigidity properties of simplicial complexes
Abstract
We give a linear upper bound on the number of distinct volume-equivalent frameworks of bipyramids, up to rigid motions. As a corollary, we show that global volume rigidity is not a generic property of simplicial complexes.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Advanced Graph Theory Research · Digital Image Processing Techniques